Approximate dynamic programming (ADP) formulation implemented with an adaptive critic (AC)-based neural network (NN) structure has evolved as a powerful technique for solving the Hamilton-Jacobi-Bellman (HJB) equations.As interest in ADP and the AC solutions are escalating with time,there is a dire need to consider possible enabling factors for their implementations.A typical AC structure consists of two interacting NNs,which is computationally expensive.In this paper,a new architecture,called the ‘cost-function-based single network adaptive critic (J-SNAC)' is presented,which eliminates one of the networks in a typical AC structure.This approach is applicable to a wide class of nonlinear systems in engineering.In order to demonstrate the benefits and the control synthesis with the J-SNAC,two problems have been solved with the AC and the J-SNAC approaches.Results are presented,which show savings of about 50％ of the computational costs by J-SNAC while having the same accuracy levels of the dual network structure in solving for optimal control.Furthermore,convergence of the J-SNAC iterations,which reduces to a least-squares problem,is discussed; for linear systems,the iterative process is shown to reduce to solving the familiar algebraic Ricatti equation.